I want to change my kitchen sink for one that is deeper. Do I need to replace all the PVC pipes or can I just cut them to make them shorter?

You can just cut one pipe, if the drain lines up.

One issue you may find installing a deeper sink, just happened on a job, is that the output of the p trap is below the wall stub out. In that case, water will pool in the sink. Make sure the p trap leg will be ABOVE the wall connection. If it is not, you will have to open the wall and lower the trap connection. In my case, the original plumber added another separate trap at the cabinet base level for the DW and I was able to connect to that. If you are lucky, you can just cut the tubing using a fine blade hacksaw or a plastic pipe cutter.